1.1 Collapse categories

Re-code sexual orientation, race, family challenge variables by collapsing some categories with limited number of samples, and generating composite categories.

1.2 Latent Class Analysis(LCA)

Apply LCA to find the latent class variables for gender identity and coping strategies, respectively.

## [1] 0.9648380 0.9863283 0.9650341

## [1] 0.8685438 0.7917650 0.9089532

1.3 Missing values

98.6% of the subjects have complete information.

Tabulate the number and percentage of missing. The missing rate is low, so complete case analysis will be used later.

Check if there is any missing pattern among missing variables: No pattern presents!

1.4 The final working dataset

After some investigation, I decided to do a complete case analysis(CCA), the final working dataset is then generated.

dat_cc <- cope_subset3 %>% 
   filter(recode_race!="Prefer not to answer") %>%  ## 1468
  filter(b_dem_sex!="Prefer not to say" & b_dem_sex!="Other") %>% ## 1447
  filter(orientation!="I do not want to respond") ## 1441

3.1 Build prediction model

Build prediction models using caret

Summary of baseline model output of project ABC model:

##             Length Class      Mode     
## a0           100   -none-     numeric  
## beta        1300   dgCMatrix  S4       
## df           100   -none-     numeric  
## dim            2   -none-     numeric  
## lambda       100   -none-     numeric  
## dev.ratio    100   -none-     numeric  
## nulldev        1   -none-     numeric  
## npasses        1   -none-     numeric  
## jerr           1   -none-     numeric  
## offset         1   -none-     logical  
## call           5   -none-     call     
## nobs           1   -none-     numeric  
## lambdaOpt      1   -none-     numeric  
## xNames        13   -none-     character
## problemType    1   -none-     character
## tuneValue      2   data.frame list     
## obsLevels      1   -none-     logical  
## param          0   -none-     list

Summary of baseline model output of project personality model:

##             Length Class      Mode     
## a0           65    -none-     numeric  
## beta        845    dgCMatrix  S4       
## df           65    -none-     numeric  
## dim           2    -none-     numeric  
## lambda       65    -none-     numeric  
## dev.ratio    65    -none-     numeric  
## nulldev       1    -none-     numeric  
## npasses       1    -none-     numeric  
## jerr          1    -none-     numeric  
## offset        1    -none-     logical  
## call          5    -none-     call     
## nobs          1    -none-     numeric  
## lambdaOpt     1    -none-     numeric  
## xNames       13    -none-     character
## problemType   1    -none-     character
## tuneValue     2    data.frame list     
## obsLevels     1    -none-     logical  
## param         0    -none-     list

3.2 Evaluate model performance

Summaries the model performance in the following table:

3.3 Final baseline prediciton model

The final model is constructed on the entire dataset

## 14 x 1 sparse Matrix of class "dgCMatrix"
##                                             s0
## (Intercept)                        1.024079643
## recode_raceBlack/African-American -0.029861721
## recode_raceHispanic/Latinx        -0.067205445
## recode_raceMixed                  -0.008337803
## recode_raceWhite                   0.041071994
## b_dem_sexMale                     -0.121873161
## recode_orientLGBTQ                 0.073487928
## recode_orientOther                 0.102386860
## genderid32                        -0.109173072
## genderid33                        -0.018497319
## family_catOther                    0.060132421
## family_catSchool                   0.020780601
## cope32                            -0.024043888
## cope33                            -0.112895337

## 14 x 1 sparse Matrix of class "dgCMatrix"
##                                             s0
## (Intercept)                        1.152897654
## recode_raceBlack/African-American -0.054500296
## recode_raceHispanic/Latinx        -0.048753462
## recode_raceMixed                  -0.030923716
## recode_raceWhite                  -0.002056701
## b_dem_sexMale                     -0.104694777
## recode_orientLGBTQ                 0.068796666
## recode_orientOther                 0.064098555
## genderid32                        -0.146439033
## genderid33                        -0.102595869
## family_catOther                    0.020356363
## family_catSchool                  -0.015311446
## cope32                            -0.054863363
## cope33                            -0.125546490

3.4 LRT

LRT was used to test the sig. of variables in the baseline model

For project ABC:

For project personality

For Project Personality

4.1 Main effect only model

first, replicate the model in the original paper for comparison. the main effect model which adjusted for baseline CDI score is specified as:\[E(Y|\bf{X}) = \text{baseline CDI}+ \text{condition}\]

print the model, compare with the published paper (results are similar): for project ABC vs control:

## 
## Call:
## lm(formula = f1_cdi_mean ~ b_cdi_mean + condition, data = abc_main_dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.18567 -0.21921  0.01075  0.22509  1.04660 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           0.27471    0.04097   6.705 3.42e-11 ***
## b_cdi_mean            0.64303    0.03263  19.706  < 2e-16 ***
## conditionProject ABC -0.07953    0.02234  -3.560 0.000389 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3492 on 974 degrees of freedom
## Multiple R-squared:  0.2922, Adjusted R-squared:  0.2907 
## F-statistic:   201 on 2 and 974 DF,  p-value: < 2.2e-16

for project personality vs control:

## 
## Call:
## lm(formula = f1_cdi_mean ~ b_cdi_mean + condition, data = person_main_dat)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.17752 -0.22054  0.01222  0.23434  1.03109 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                   0.31125    0.04188   7.432 2.38e-13 ***
## b_cdi_mean                    0.61148    0.03329  18.366  < 2e-16 ***
## conditionProject Personality -0.06895    0.02337  -2.950  0.00325 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3604 on 949 degrees of freedom
## Multiple R-squared:  0.2664, Adjusted R-squared:  0.2649 
## F-statistic: 172.3 on 2 and 949 DF,  p-value: < 2.2e-16

4.2 HTE model

The HTE is defined as: \[E(Y|\bf{X}) = \text{baseline CDI}+ \text{condition} + \text{lp}+\text{condition}\times \text{lp}\] where lp is the linear predictor of the baseline model.

## 
## Call:
## lm(formula = f1_cdi_mean ~ b_cdi_mean + condition * lp_abc, data = dat_abc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.16587 -0.21245  0.01587  0.22319  1.04761 
## 
## Coefficients:
##                             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                  0.20672    0.13296   1.555   0.1203    
## b_cdi_mean                   0.60042    0.03517  17.070   <2e-16 ***
## conditionProject ABC        -0.46326    0.18742  -2.472   0.0136 *  
## lp_abc                       0.11985    0.14022   0.855   0.3929    
## conditionProject ABC:lp_abc  0.39263    0.19023   2.064   0.0393 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3471 on 972 degrees of freedom
## Multiple R-squared:  0.302,  Adjusted R-squared:  0.2991 
## F-statistic: 105.1 on 4 and 972 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = f1_cdi_mean ~ b_cdi_mean + condition * lp_person, 
##     data = dat_person)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.1604 -0.2189  0.0176  0.2321  1.0427 
## 
## Coefficients:
##                                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                             0.18881    0.16684   1.132    0.258    
## b_cdi_mean                              0.58760    0.03544  16.580   <2e-16 ***
## conditionProject Personality           -0.28385    0.24270  -1.170    0.242    
## lp_person                               0.15184    0.17399   0.873    0.383    
## conditionProject Personality:lp_person  0.21744    0.24431   0.890    0.374    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3599 on 947 degrees of freedom
## Multiple R-squared:   0.27,  Adjusted R-squared:  0.2669 
## F-statistic: 87.56 on 4 and 947 DF,  p-value: < 2.2e-16

5.1 Point estiamtes

First, report the point estiamtes of ATE and cATE.

A brief summary of the linear predictors:

## Length  Class   Mode 
##      0   NULL   NULL

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.7486  0.9316  0.9751  0.9888  1.0464  1.2441

5.2 Bootstrapped CI

compute bootstrapped CI for cATE:

for Project personality:

5.3 Calibration plots

The linear predictor entered model as a continuous variable. For presentation purpose, the linear predictor is discretized into five “risk” groups using quantiles (0.2 incremental). The averaged HTEs/cATEs by “risk” group are calculated and compared with the ATE.

For Project ABC vs control:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.6620  0.8980  0.9743  0.9782  1.0605  1.2931

For Project personality vs control:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.7486  0.9316  0.9751  0.9888  1.0464  1.2441

combined plots for reporting purpose:

## Joining with `by = join_by(quantile_grp)`

## Joining with `by = join_by(quantile_grp)`

5.4 Distribution in high risk groups

## % latex table generated in R 4.3.1 by xtable 1.8-4 package
## % Fri Aug  2 17:40:22 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{lllllllllll}
##   \hline
## **Demographics** & **1**  
## N = 98 & **10**  
## N = 94 & **2**  
## N = 104 & **3**  
## N = 92 & **4**  
## N = 97 & **5**  
## N = 101 & **6**  
## N = 95 & **7**  
## N = 103 & **8**  
## N = 91 & **9**  
## N = 102 \\ 
##   \hline
## condition &  &  &  &  &  &  &  &  &  &  \\ 
##   Placebo Control & 44 (45\%) & 42 (45\%) & 57 (55\%) & 52 (57\%) & 51 (53\%) & 44 (44\%) & 41 (43\%) & 51 (50\%) & 45 (49\%) & 61 (60\%) \\ 
##   Project ABC & 54 (55\%) & 52 (55\%) & 47 (45\%) & 40 (43\%) & 46 (47\%) & 57 (56\%) & 54 (57\%) & 52 (50\%) & 46 (51\%) & 41 (40\%) \\ 
##   Baseline CDI mean score(0-2) & 0.92 (0.31) & 1.37 (0.30) & 1.04 (0.37) & 1.06 (0.33) & 1.05 (0.29) & 1.14 (0.34) & 1.23 (0.31) & 1.21 (0.30) & 1.26 (0.32) & 1.29 (0.30) \\ 
##   Race &  &  &  &  &  &  &  &  &  &  \\ 
##   Asian Including Asian Desi & 18 (18\%) & 1 (1.1\%) & 13 (13\%) & 35 (38\%) & 3 (3.1\%) & 9 (8.9\%) & 10 (11\%) & 9 (8.7\%) & 5 (5.5\%) & 5 (4.9\%) \\ 
##   Black/African-American & 16 (16\%) & 4 (4.3\%) & 16 (15\%) & 5 (5.4\%) & 5 (5.2\%) & 11 (11\%) & 8 (8.4\%) & 3 (2.9\%) & 3 (3.3\%) & 2 (2.0\%) \\ 
##   Hispanic/Latinx & 38 (39\%) & 1 (1.1\%) & 27 (26\%) & 1 (1.1\%) & 16 (16\%) & 20 (20\%) & 2 (2.1\%) & 3 (2.9\%) & 5 (5.5\%) & 5 (4.9\%) \\ 
##   Mixed & 10 (10\%) & 14 (15\%) & 26 (25\%) & 1 (1.1\%) & 13 (13\%) & 17 (17\%) & 21 (22\%) & 11 (11\%) & 12 (13\%) & 17 (17\%) \\ 
##   White & 16 (16\%) & 74 (79\%) & 22 (21\%) & 50 (54\%) & 60 (62\%) & 44 (44\%) & 54 (57\%) & 77 (75\%) & 66 (73\%) & 73 (72\%) \\ 
##   Age (yrs) &  &  &  &  &  &  &  &  &  &  \\ 
##   13 & 3 (3.1\%) & 10 (11\%) & 4 (3.8\%) & 1 (1.1\%) & 5 (5.2\%) & 6 (5.9\%) & 7 (7.4\%) & 8 (7.8\%) & 9 (9.9\%) & 7 (6.9\%) \\ 
##   14 & 12 (12\%) & 16 (17\%) & 13 (13\%) & 19 (21\%) & 11 (11\%) & 21 (21\%) & 15 (16\%) & 12 (12\%) & 20 (22\%) & 19 (19\%) \\ 
##   15 & 32 (33\%) & 30 (32\%) & 30 (29\%) & 29 (32\%) & 27 (28\%) & 28 (28\%) & 27 (28\%) & 39 (38\%) & 27 (30\%) & 37 (36\%) \\ 
##   16 & 51 (52\%) & 38 (40\%) & 57 (55\%) & 43 (47\%) & 54 (56\%) & 46 (46\%) & 46 (48\%) & 44 (43\%) & 35 (38\%) & 39 (38\%) \\ 
##   Biological sex &  &  &  &  &  &  &  &  &  &  \\ 
##   Female & 66 (67\%) & 94 (100\%) & 83 (80\%) & 80 (87\%) & 87 (90\%) & 92 (91\%) & 80 (84\%) & 101 (98\%) & 87 (96\%) & 101 (99\%) \\ 
##   Male & 32 (33\%) & 0 (0\%) & 21 (20\%) & 12 (13\%) & 10 (10\%) & 9 (8.9\%) & 15 (16\%) & 2 (1.9\%) & 4 (4.4\%) & 1 (1.0\%) \\ 
##   Sexual orientation &  &  &  &  &  &  &  &  &  &  \\ 
##   Heterosexual & 77 (79\%) & 0 (0\%) & 45 (43\%) & 39 (42\%) & 5 (5.2\%) & 20 (20\%) & 16 (17\%) & 0 (0\%) & 3 (3.3\%) & 0 (0\%) \\ 
##   LGBTQ & 20 (20\%) & 64 (68\%) & 57 (55\%) & 48 (52\%) & 83 (86\%) & 68 (67\%) & 75 (79\%) & 90 (87\%) & 54 (59\%) & 77 (75\%) \\ 
##   Other & 1 (1.0\%) & 30 (32\%) & 2 (1.9\%) & 5 (5.4\%) & 9 (9.3\%) & 13 (13\%) & 4 (4.2\%) & 13 (13\%) & 34 (37\%) & 25 (25\%) \\ 
##   Language &  &  &  &  &  &  &  &  &  &  \\ 
##   English & 91 (93\%) & 93 (99\%) & 100 (96\%) & 88 (96\%) & 94 (97\%) & 99 (98\%) & 94 (99\%) & 102 (99\%) & 91 (100\%) & 100 (98\%) \\ 
##   Other & 7 (7.1\%) & 1 (1.1\%) & 4 (3.8\%) & 4 (4.3\%) & 3 (3.1\%) & 2 (2.0\%) & 1 (1.1\%) & 1 (1.0\%) & 0 (0\%) & 2 (2.0\%) \\ 
##   Gender identity &  &  &  &  &  &  &  &  &  &  \\ 
##   Non-binary & 1 (1.0\%) & 79 (84\%) & 2 (1.9\%) & 1 (1.1\%) & 5 (5.2\%) & 5 (5.0\%) & 20 (21\%) & 10 (9.7\%) & 27 (30\%) & 50 (49\%) \\ 
##   Women/girls & 70 (71\%) & 0 (0\%) & 83 (80\%) & 80 (87\%) & 86 (89\%) & 88 (87\%) & 61 (64\%) & 87 (84\%) & 48 (53\%) & 35 (34\%) \\ 
##   Male/Masculine & 27 (28\%) & 15 (16\%) & 19 (18\%) & 11 (12\%) & 6 (6.2\%) & 8 (7.9\%) & 14 (15\%) & 6 (5.8\%) & 16 (18\%) & 17 (17\%) \\ 
##   Number of challenges &  &  &  &  &  &  &  &  &  &  \\ 
##   0 & 26 (27\%) & 8 (8.5\%) & 31 (30\%) & 37 (40\%) & 9 (9.3\%) & 9 (8.9\%) & 30 (32\%) & 16 (16\%) & 17 (19\%) & 14 (14\%) \\ 
##   1 & 58 (59\%) & 44 (47\%) & 65 (63\%) & 46 (50\%) & 77 (79\%) & 58 (57\%) & 44 (46\%) & 74 (72\%) & 47 (52\%) & 60 (59\%) \\ 
##   $>$=2 & 14 (14\%) & 42 (45\%) & 8 (7.7\%) & 9 (9.8\%) & 11 (11\%) & 34 (34\%) & 21 (22\%) & 13 (13\%) & 27 (30\%) & 28 (27\%) \\ 
##   Type of challenges &  &  &  &  &  &  &  &  &  &  \\ 
##   No impact & 26 (27\%) & 8 (8.5\%) & 31 (30\%) & 37 (40\%) & 9 (9.3\%) & 9 (8.9\%) & 30 (32\%) & 16 (16\%) & 17 (19\%) & 14 (14\%) \\ 
##   Other & 11 (11\%) & 45 (48\%) & 10 (9.6\%) & 12 (13\%) & 9 (9.3\%) & 33 (33\%) & 27 (28\%) & 6 (5.8\%) & 25 (27\%) & 38 (37\%) \\ 
##   School & 61 (62\%) & 41 (44\%) & 63 (61\%) & 43 (47\%) & 79 (81\%) & 59 (58\%) & 38 (40\%) & 81 (79\%) & 49 (54\%) & 50 (49\%) \\ 
##   Type of coping strategies &  &  &  &  &  &  &  &  &  &  \\ 
##   Combined & 0 (0\%) & 35 (37\%) & 0 (0\%) & 0 (0\%) & 2 (2.1\%) & 7 (6.9\%) & 9 (9.5\%) & 13 (13\%) & 17 (19\%) & 36 (35\%) \\ 
##   No action & 11 (11\%) & 59 (63\%) & 39 (38\%) & 33 (36\%) & 25 (26\%) & 62 (61\%) & 67 (71\%) & 78 (76\%) & 47 (52\%) & 42 (41\%) \\ 
##   Positive & 87 (89\%) & 0 (0\%) & 65 (63\%) & 59 (64\%) & 70 (72\%) & 32 (32\%) & 19 (20\%) & 12 (12\%) & 27 (30\%) & 24 (24\%) \\ 
##   abc\_ate &  &  &  &  &  &  &  &  &  &  \\ 
##   -0.0795346966023499 & 98 (100\%) & 94 (100\%) & 104 (100\%) & 92 (100\%) & 97 (100\%) & 101 (100\%) & 95 (100\%) & 103 (100\%) & 91 (100\%) & 102 (100\%) \\ 
##   abc\_hte & -0.16 (0.01) & 0.00 (0.02) & -0.13 (0.01) & -0.11 (0.00) & -0.10 (0.00) & -0.09 (0.00) & -0.07 (0.00) & -0.06 (0.00) & -0.05 (0.00) & -0.03 (0.01) \\ 
##   lp\_abc & 0.78 (0.03) & 1.19 (0.04) & 0.86 (0.02) & 0.90 (0.01) & 0.92 (0.01) & 0.96 (0.01) & 1.00 (0.01) & 1.03 (0.00) & 1.06 (0.01) & 1.11 (0.02) \\ 
##    \hline
## \end{tabular}
## \end{table}

## % latex table generated in R 4.3.1 by xtable 1.8-4 package
## % Fri Aug  2 17:40:24 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{lllllllllll}
##   \hline
## **Demographics** & **1**  
## N = 101 & **10**  
## N = 96 & **2**  
## N = 94 & **3**  
## N = 103 & **4**  
## N = 83 & **5**  
## N = 95 & **6**  
## N = 120 & **7**  
## N = 72 & **8**  
## N = 94 & **9**  
## N = 94 \\ 
##   \hline
## condition &  &  &  &  &  &  &  &  &  &  \\ 
##   Placebo Control & 56 (55\%) & 46 (48\%) & 53 (56\%) & 46 (45\%) & 44 (53\%) & 47 (49\%) & 63 (53\%) & 33 (46\%) & 46 (49\%) & 54 (57\%) \\ 
##   Project Personality & 45 (45\%) & 50 (52\%) & 41 (44\%) & 57 (55\%) & 39 (47\%) & 48 (51\%) & 57 (48\%) & 39 (54\%) & 48 (51\%) & 40 (43\%) \\ 
##   Baseline CDI mean score(0-2) & 0.93 (0.32) & 1.35 (0.30) & 1.02 (0.39) & 1.06 (0.33) & 1.12 (0.37) & 1.19 (0.31) & 1.19 (0.28) & 1.25 (0.30) & 1.24 (0.36) & 1.29 (0.33) \\ 
##   Race &  &  &  &  &  &  &  &  &  &  \\ 
##   Asian Including Asian Desi & 11 (11\%) & 6 (6.3\%) & 9 (9.6\%) & 3 (2.9\%) & 26 (31\%) & 15 (16\%) & 5 (4.2\%) & 15 (21\%) & 2 (2.1\%) & 8 (8.5\%) \\ 
##   Black/African-American & 14 (14\%) & 3 (3.1\%) & 12 (13\%) & 12 (12\%) & 8 (9.6\%) & 5 (5.3\%) & 4 (3.3\%) & 3 (4.2\%) & 2 (2.1\%) & 6 (6.4\%) \\ 
##   Hispanic/Latinx & 20 (20\%) & 3 (3.1\%) & 26 (28\%) & 8 (7.8\%) & 0 (0\%) & 24 (25\%) & 13 (11\%) & 5 (6.9\%) & 3 (3.2\%) & 8 (8.5\%) \\ 
##   Mixed & 9 (8.9\%) & 14 (15\%) & 23 (24\%) & 10 (9.7\%) & 9 (11\%) & 12 (13\%) & 9 (7.5\%) & 19 (26\%) & 17 (18\%) & 15 (16\%) \\ 
##   White & 47 (47\%) & 70 (73\%) & 24 (26\%) & 70 (68\%) & 40 (48\%) & 39 (41\%) & 89 (74\%) & 30 (42\%) & 70 (74\%) & 57 (61\%) \\ 
##   Age (yrs) &  &  &  &  &  &  &  &  &  &  \\ 
##   13 & 3 (3.0\%) & 7 (7.3\%) & 4 (4.3\%) & 1 (1.0\%) & 3 (3.6\%) & 10 (11\%) & 9 (7.5\%) & 7 (9.7\%) & 7 (7.4\%) & 5 (5.3\%) \\ 
##   14 & 15 (15\%) & 17 (18\%) & 11 (12\%) & 18 (17\%) & 15 (18\%) & 9 (9.5\%) & 15 (13\%) & 13 (18\%) & 13 (14\%) & 14 (15\%) \\ 
##   15 & 39 (39\%) & 28 (29\%) & 28 (30\%) & 34 (33\%) & 25 (30\%) & 31 (33\%) & 37 (31\%) & 23 (32\%) & 32 (34\%) & 35 (37\%) \\ 
##   16 & 44 (44\%) & 44 (46\%) & 51 (54\%) & 50 (49\%) & 40 (48\%) & 45 (47\%) & 59 (49\%) & 29 (40\%) & 42 (45\%) & 40 (43\%) \\ 
##   Biological sex &  &  &  &  &  &  &  &  &  &  \\ 
##   Female & 58 (57\%) & 96 (100\%) & 77 (82\%) & 94 (91\%) & 78 (94\%) & 87 (92\%) & 113 (94\%) & 71 (99\%) & 87 (93\%) & 91 (97\%) \\ 
##   Male & 43 (43\%) & 0 (0\%) & 17 (18\%) & 9 (8.7\%) & 5 (6.0\%) & 8 (8.4\%) & 7 (5.8\%) & 1 (1.4\%) & 7 (7.4\%) & 3 (3.2\%) \\ 
##   Sexual orientation &  &  &  &  &  &  &  &  &  &  \\ 
##   Heterosexual & 86 (85\%) & 0 (0\%) & 44 (47\%) & 29 (28\%) & 27 (33\%) & 18 (19\%) & 7 (5.8\%) & 3 (4.2\%) & 0 (0\%) & 0 (0\%) \\ 
##   LGBTQ & 13 (13\%) & 66 (69\%) & 45 (48\%) & 66 (64\%) & 51 (61\%) & 63 (66\%) & 87 (73\%) & 58 (81\%) & 76 (81\%) & 75 (80\%) \\ 
##   Other & 2 (2.0\%) & 30 (31\%) & 5 (5.3\%) & 8 (7.8\%) & 5 (6.0\%) & 14 (15\%) & 26 (22\%) & 11 (15\%) & 18 (19\%) & 19 (20\%) \\ 
##   Language &  &  &  &  &  &  &  &  &  &  \\ 
##   English & 94 (93\%) & 94 (98\%) & 90 (96\%) & 100 (97\%) & 80 (96\%) & 92 (97\%) & 119 (99\%) & 70 (97\%) & 94 (100\%) & 93 (99\%) \\ 
##   Other & 7 (6.9\%) & 2 (2.1\%) & 4 (4.3\%) & 3 (2.9\%) & 3 (3.6\%) & 3 (3.2\%) & 1 (0.8\%) & 2 (2.8\%) & 0 (0\%) & 1 (1.1\%) \\ 
##   Gender identity &  &  &  &  &  &  &  &  &  &  \\ 
##   Non-binary & 0 (0\%) & 91 (95\%) & 0 (0\%) & 2 (1.9\%) & 0 (0\%) & 2 (2.1\%) & 3 (2.5\%) & 3 (4.2\%) & 20 (21\%) & 67 (71\%) \\ 
##   Women/girls & 61 (60\%) & 0 (0\%) & 77 (82\%) & 93 (90\%) & 78 (94\%) & 82 (86\%) & 95 (79\%) & 61 (85\%) & 55 (59\%) & 17 (18\%) \\ 
##   Male/Masculine & 40 (40\%) & 5 (5.2\%) & 17 (18\%) & 8 (7.8\%) & 5 (6.0\%) & 11 (12\%) & 22 (18\%) & 8 (11\%) & 19 (20\%) & 10 (11\%) \\ 
##   Number of challenges &  &  &  &  &  &  &  &  &  &  \\ 
##   0 & 10 (9.9\%) & 20 (21\%) & 27 (29\%) & 4 (3.9\%) & 37 (45\%) & 20 (21\%) & 15 (13\%) & 25 (35\%) & 11 (12\%) & 14 (15\%) \\ 
##   1 & 78 (77\%) & 39 (41\%) & 56 (60\%) & 77 (75\%) & 37 (45\%) & 48 (51\%) & 85 (71\%) & 30 (42\%) & 58 (62\%) & 43 (46\%) \\ 
##   $>$=2 & 13 (13\%) & 37 (39\%) & 11 (12\%) & 22 (21\%) & 9 (11\%) & 27 (28\%) & 20 (17\%) & 17 (24\%) & 25 (27\%) & 37 (39\%) \\ 
##   Type of challenges &  &  &  &  &  &  &  &  &  &  \\ 
##   No impact & 10 (9.9\%) & 20 (21\%) & 27 (29\%) & 4 (3.9\%) & 37 (45\%) & 20 (21\%) & 15 (13\%) & 25 (35\%) & 11 (12\%) & 14 (15\%) \\ 
##   Other & 11 (11\%) & 37 (39\%) & 10 (11\%) & 21 (20\%) & 9 (11\%) & 37 (39\%) & 19 (16\%) & 19 (26\%) & 39 (41\%) & 41 (44\%) \\ 
##   School & 80 (79\%) & 39 (41\%) & 57 (61\%) & 78 (76\%) & 37 (45\%) & 38 (40\%) & 86 (72\%) & 28 (39\%) & 44 (47\%) & 39 (41\%) \\ 
##   Type of coping strategies &  &  &  &  &  &  &  &  &  &  \\ 
##   Combined & 0 (0\%) & 31 (32\%) & 0 (0\%) & 0 (0\%) & 2 (2.4\%) & 1 (1.1\%) & 8 (6.7\%) & 15 (21\%) & 29 (31\%) & 25 (27\%) \\ 
##   No action & 16 (16\%) & 65 (68\%) & 28 (30\%) & 33 (32\%) & 36 (43\%) & 63 (66\%) & 95 (79\%) & 49 (68\%) & 50 (53\%) & 29 (31\%) \\ 
##   Positive & 85 (84\%) & 0 (0\%) & 66 (70\%) & 70 (68\%) & 45 (54\%) & 31 (33\%) & 17 (14\%) & 8 (11\%) & 15 (16\%) & 40 (43\%) \\ 
##   person\_ate &  &  &  &  &  &  &  &  &  &  \\ 
##   -0.0689513014845681 & 101 (100\%) & 96 (100\%) & 94 (100\%) & 103 (100\%) & 83 (100\%) & 95 (100\%) & 120 (100\%) & 72 (100\%) & 94 (100\%) & 94 (100\%) \\ 
##   person\_hte & -0.10 (0.01) & -0.03 (0.01) & -0.09 (0.00) & -0.08 (0.00) & -0.08 (0.00) & -0.07 (0.00) & -0.07 (0.00) & -0.06 (0.00) & -0.06 (0.00) & -0.04 (0.00) \\ 
##   lp\_person & 0.84 (0.03) & 1.17 (0.03) & 0.89 (0.01) & 0.93 (0.01) & 0.94 (0.01) & 0.96 (0.01) & 1.00 (0.01) & 1.01 (0.01) & 1.05 (0.01) & 1.10 (0.02) \\ 
##    \hline
## \end{tabular}
## \end{table}

6.1 inverse probability of missingness weighting (IPMW)

Check the missingness, and regress the missing status on variables with complete info.

## .
##    0    1 
## 1441   60

## tibble [1,501 × 10] (S3: tbl_df/tbl/data.frame)
##  $ condition    : chr [1:1501] "Placebo Control" "Project Personality" "Placebo Control" "Placebo Control" ...
##  $ b_cdi_mean   : num [1:1501] 1.417 0.917 1.167 1.333 0.917 ...
##  $ f1_cdi_mean  : num [1:1501] 1 0.583 0.583 1.417 0.5 ...
##  $ recode_race  : Factor w/ 5 levels "Asian Including Asian Desi",..: 5 5 5 5 5 5 1 1 5 4 ...
##  $ b_dem_sex    : Factor w/ 2 levels "Female","Male": 1 1 1 1 1 1 1 1 1 1 ...
##  $ recode_orient: Factor w/ 3 levels "Heterosexual",..: 2 3 2 2 2 2 1 2 1 2 ...
##  $ genderid3    : Factor w/ 3 levels "1","2","3": 1 1 2 2 2 3 2 2 2 2 ...
##  $ family_cat   : Factor w/ 3 levels "No impact","Other",..: 2 2 1 3 3 3 3 3 3 2 ...
##  $ cope3        : Factor w/ 3 levels "1","2","3": 3 3 3 2 1 2 2 2 2 2 ...
##  $ missing      : num [1:1501] 0 0 0 0 0 0 0 0 0 0 ...

A summary of the IPCW model:

## 
## Call:
## glm(formula = missing ~ genderid3 + b_cdi_mean + family_cat + 
##     cope3, family = "binomial", data = model_dat)
## 
## Coefficients:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)       -3.0919     0.8430  -3.668 0.000245 ***
## genderid32        -1.2368     0.2870  -4.309 1.64e-05 ***
## genderid33        -1.2284     0.4630  -2.653 0.007978 ** 
## b_cdi_mean         0.2561     0.4193   0.611 0.541408    
## family_catOther   -0.1730     0.3659  -0.473 0.636328    
## family_catSchool  -0.5263     0.3270  -1.610 0.107490    
## cope32             0.9205     0.5452   1.688 0.091346 .  
## cope33             0.7123     0.5729   1.243 0.213729    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 503.91  on 1500  degrees of freedom
## Residual deviance: 476.46  on 1493  degrees of freedom
## AIC: 492.46
## 
## Number of Fisher Scoring iterations: 6

Summary of IPCW weights:

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9687  0.9815  0.9878  1.0000  1.0002  1.1427

6.2 Baseline prediction models

6.3 Main effect model

6.4 The HTE models

6.5 Risk stratification

6.6 Boot CI

For Project ABC:

For Project personality:

6.7 Risk stratification

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.6620  0.8980  0.9743  0.9782  1.0605  1.2931

Distribution of baseline depression severity score